Towards an exact orbital-free single-particle kinetic energy density for the inhomogeneous electron liquid in the Be atom

Holas and March (Phys. Rev. A51, 2040 (1995)) wrote the gradient of the one-body potential V(r) in terms of low-order derivatives of the idempotent Dirac density matrix built from a single Slater determinant of Kohn-Sham orbitals. Here, this is first combined with the study of Dawson and March (J. Chem. Phys. 81, 5850 (1984)) to express the single-particle kinetic energy density of the Be atom ground-state in terms of both the electron density n(r) and potential V(r). While this is the more compact formulation, we then, by removing V(r), demonstrate that the ratio t(r)/n(r) depends, though non-locally, only on the single variable n'(r)/n(r), no high-order gradients entering for the spherical Be atom.Comment: Submitted to Journal of Mathematical Chemistr

Investigation of the chirality of enantiomers through information theory

In this work [1] we probed the Kullback-Leibler information entropy as a chirality measure, as an extension of previous studies on molecular quantum similarity evaluated for different enantiomers (enantiomers possessing two asymmetric centra in [2], with a single asymmetric carbon atom in [3] and with a chiral axis in [4]). The entropy was calculated using the shape functions of the R and S enantiomers considering one as reference for the other, resulting in an information theory based expression useful for quantifying chirality. It was evaluated for 5 chiral halomethanes possessing one asymmetric carbon atom with H, F, Cl, Br and I as substituents. To demonstrate the general applicability, a study of two halogen-substituted ethanes possessing two asymmetric carbon atoms has been included as well. Avnir’s Continuous Chirality Measure (CCM) [5] has been computed and confronted with the information deficiency. By these means we quantified the dissimilarity of enantiomers and illustrated Mezey’s Holographic Electron Density Theorem in chiral systems [6]. A comparison is made with the optical rotation and with the Carbó similarity index. As an alternative chirality index, we recently also calculated the information deficiency in a way which is consistent with experiments as VCD spectroscopy and optical rotation measurements. The entropy calculates the difference in information between the shape function of one enantiomer and a normalized shape function of the racemate. Comparing the latter index with the optical rotation reveals a similar trend. [1] S. Janssens, A. Borgoo, C. Van Alsenoy, P. Geerlings, J. Phys. Chem. A, 112, 10560 (2008). [2] S. Janssens, C. Van Alsenoy, P. Geerlings, J. Phys. Chem. A, 111, 3143 (2007). [3] G. Boon, C. Van Alsenoy, F. De Proft, P. Bultinck, P. Geerlings, J. Phys. Chem. A, 110, 5114 (2006). [4] S. Janssens, G. Boon, P. Geerlings, J. Phys. Chem. A, 110, 9267 (2006). [5] H. Zabrodsky, D. Avnir, J. Am. Chem. Soc., 117, 462 (1995). [6] P.G. Mezey, Mol. Phys., 96, 169 (1999)

Alternative Kullback-Leibler information entropy for enantiomers

In our series of studies on quantifying chirality, a new chirality measure is proposed in this work based on the Kullback-Leibler information entropy. The index computes the extra information that the shape function of one enantiomer carries over a normalized shape function of the racemate, while in our previous studies the shape functions of the R and S enantiomers were used considering one as reference for the other. Besides being mathematically more elegant (symmetric, positive definite, zero in the case of a nonchiral system), this new index bears a more direct relation with chirality oriented experimental measurements such as circular dichroism (CD) and optical rotation measurements, where the racemate is frequently used as a reference, The five chiral halomethanes holding one asymmetric carbon atom and H, F, Cl, Br, and I as substituents have been analyzed. A comparison with our calculated optical rotation and with Avnir's Continuous Chirality Measure (CCM) is computed. The results show that with this index the emphasis lies on the differences between the noncoinciding substituents

Quantum similarity of isosteres coordinate versus momentum space and influence of alignment

A

An Overview of Self-Consistent Field Calculations Within Finite Basis Sets

A uniform derivation of the self-consistent field equations in a finite basis set is presented. Both restricted and unrestricted Hartree–Fock (HF) theory as well as various density functional approximations are considered. The unitary invariance of the HF and density functional models is discussed, paving the way for the use of localized molecular orbitals. The self-consistent field equations are derived in a non-orthogonal basis set, and their solution is discussed also in the presence of linear dependencies in the basis. It is argued why iterative diagonalization of the Kohn–Sham–Fock matrix leads to the minimization of the total energy. Alternative methods for the solution of the self-consistent field equations via direct minimization as well as stability analysis are briefly discussed. Explicit expressions are given for the contributions to the Kohn–Sham–Fock matrix up to meta-GGA functionals. Range-separated hybrids and non-local correlation functionals are summarily reviewed

Accurate interaction energies at DFT level by means of an efficient dispersion correction

This paper presents an approach for obtaining accurate interaction energies at the DFT level for systems where dispersion interactions are important. This approach combines Becke and Johnson's [J. Chem. Phys. 127, 154108 (2007)] method for the evaluation of dispersion energy corrections and a Hirshfeld method for partitioning of molecular polarizability tensors into atomic contributions. Due to the availability of atomic polarizability tensors, the method is extended to incorporate anisotropic contributions, which prove to be important for complexes of lower symmetry. The method is validated for a set of eighteen complexes, for which interaction energies were obtained with the B3LYP, PBE and TPSS functionals combined with the aug-cc-pVTZ basis set and compared with the values obtained at CCSD(T) level extrapolated to a complete basis set limit. It is shown that very good quality interaction energies can be obtained by the proposed method for each of the examined functionals, the overall performance of the TPSS functional being the best, which with a slope of 1.00 in the linear regression equation and a constant term of only 0.1 kcal/mol allows to obtain accurate interaction energies without any need of a damping function for complexes close to their exact equilibrium geometry

Local softness, softness dipole and polarizabilities of functional groups: application to the side chains of the twenty amino acids

The values of molecular polarizabilities and softnesses of the twenty amino acids were computed ab initio (MP2). By using the iterative Hirshfeld scheme to partition the molecular electronic properties, we demonstrate that the values of the softness of the side chain of the twenty amino acid are clustered in groups reflecting their biochemical classification, namely: aliphatic, basic, acidic, sulfur containing, and aromatic amino acids . The present findings are in agreement with previous results using different approximations and partitioning schemes [P. Senet and F. Aparicio, J. Chem. Phys. 126,145105 (2007)]. In addition, we show that the polarizability of the side chain of an amino acid depends mainly on its number of electrons (reflecting its size) and consequently cannot be used to cluster the amino acids in different biochemical groups, in contrast to the local softness. Our results also demonstrate that the global softness is not simply proportional to the global polarizability in disagreement with the intuition that "a softer moiety is also more polarizable". Amino acids with the same softness may have a polarizability differing by a factor as large as 1.7. This discrepancy can be understood from first principles as we show that the molecular polarizability depends on a "softness dipole vector" and not simply on the global softness